Supermatrix Representations of Semigroup Bands

Steven Duplij

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arXiv · funct-an/9609002

Supermatrix Representations of Semigroup Bands

Steven Duplij

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Abstract

Various semigroups of noninvertible supermatrices of the special (antitriangle) shape having nilpotent Berezinian which appear in supersymmetric theories are defined and investigated. A subset of them continuously represents left and right zero semigroups and rectangular bands. The ideal properties of higher order rectangular band analogs and the ``wreath'' version of them are studied in detail. We introduce the ``fine'' equivalence relations leading to ``multidimesional'' eggbox diagrams. They are full images of Green's relations on corresponding subsemigroups.

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Steven Duplij. 1996-09-19. Supermatrix Representations of Semigroup Bands. https://arxiv.org/abs/funct-an/9609002

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